They included HMP Whitemoor, a category A jail in Cambridgeshire, which had four spaces left, according to the latest data published by the Ministry of Justice (MoJ).

Other prisons in the region, including HMP Bure, near Norwich, also faced similar pressure.

The MoJ said £2.3bn had been pledged towards building prisons over the next two years, and it aimed to open up 14,000 places by 2031.

The figures, accurate at the end of November, showed Whitemoor was four inmates below its operational capacity of 458 inmates.

HMP Rye Hill, a category B prison in Northamptonshire, had just two vacant cells – despite the situation being the same in March.

HMP Peterborough, which accommodates both male and female prisoners, had 52 spaces left at its 1,304-inmate capacity, according to the data.

In Suffolk, HMP Warren Hill had three spaces left, while HMP Highpoint had 11.

The Mount, in Hertfordshire, had room for seven more prisoners inside its 1,032-capacity site.

Pressure at HMP Chelmsford, in Essex, eased since March, with figures showing the category B facility was 42 inmates shy of its 723 capacity by December.

Separate MoJ data, published on 16 December, revealed there were 85,960 prison spaces left in England and Wales – with an overall operational capacity of 88,692.

Unveiling extra funding to build prisons, justice secretary Shabana Mahmood said Labour inherited a prison system “on the edge of collapse”.

“This capacity strategy, alongside an independent review of sentencing policy, will keep our streets safe and ensure no government runs out of prison places again,” she said.

Prisons were due to be deemed as sites of national importance under new planning rules, an MoJ spokesman added.

The move would bust “lengthy delays” stopping new prisons being built quickly, he said.

Earlier this year, the government released certain offenders early to ease overcrowding in prisons.